Subgroups — C₂×#72231700 #72310632

Order 2048.

At least 11656 conjugacy classes of subgroups; only the 1168 normal subgroups are shown.

The subgroup lattice has 621 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#500158	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#512046	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#130785	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#129613	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10583240	C₂	1	1	yes	maximal, characteristic
6	C₂×#130290	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#486694	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#486689	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#130288	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#130296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#486701	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#130782	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#130776	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#500168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#500164	C₂	1	1	yes	maximal, characteristic, complemented
16	#72231700	C₂	1	16	yes	maximal, direct product factor
17	#10583240	C₂²	1	8	yes	—
18	C₂×#62334	C₂²	1	1	yes	characteristic
19	C₂×#62283	C₂²	1	1	yes	characteristic
20	C₂×#62269	C₂²	1	1	yes	characteristic
21	C₂×#61079	C₂²	1	1	yes	characteristic
22	C₂×#61063	C₂²	1	1	yes	characteristic
23	C₂×#61049	C₂²	1	1	yes	characteristic
24	C₂×#60314	C₂²	1	1	yes	characteristic
25	C₂×#33659	C₂²	1	1	yes	characteristic, complemented
26	C₂×#33659	C₂²	1	1	yes	characteristic, complemented
27	C₂×#33657	C₂²	1	1	yes	characteristic, complemented
28	C₂×#33392	C₂²	1	1	yes	characteristic, complemented
29	C₂×#27694	C₂²	1	1	yes	characteristic, complemented
30	C₂×#27692	C₂²	1	1	yes	characteristic, complemented
31	C₂×#27691	C₂²	1	1	yes	characteristic, complemented
32	#512046	C₂²	1	8	yes	complemented
33	#500168	C₂²	1	8	yes	complemented
34	#500164	C₂²	1	8	yes	complemented
35	#500158	C₂²	1	8	yes	complemented
36	C₂×#13079	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13077	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13076	C₂²	1	1	yes	characteristic, complemented
39	C₂×#12989	C₂²	1	1	yes	characteristic, complemented
40	C₂×#12988	C₂²	1	1	yes	characteristic, complemented
41	C₂×#12981	C₂²	1	1	yes	characteristic, complemented
42	C₂×#12810	C₂²	1	1	yes	characteristic, complemented
43	C₂×#12806	C₂²	1	1	yes	characteristic, complemented
44	C₂×#12805	C₂²	1	1	yes	characteristic, complemented
45	C₂×#12743	C₂²	1	1	yes	characteristic, complemented
46	C₂×#12743	C₂²	1	1	yes	characteristic, complemented
47	C₂×#12741	C₂²	1	1	yes	characteristic, complemented
48	#486701	C₂²	1	8	yes	complemented
49	#486694	C₂²	1	8	yes	complemented
50	#486689	C₂²	1	8	yes	complemented
51	C₂×#11872	C₂²	1	1	yes	characteristic, complemented
52	C₂×#11872	C₂²	1	1	yes	characteristic, complemented
53	C₂×#11872	C₂²	1	1	yes	characteristic, complemented
54	C₂×#11870	C₂²	1	1	yes	characteristic, complemented
55	C₂×#11867	C₂²	1	1	yes	characteristic, complemented
56	C₂×#11868	C₂²	1	1	yes	characteristic, complemented
57	C₂×#11486	C₂²	1	1	yes	characteristic, complemented
58	C₂×#11484	C₂²	1	1	yes	characteristic, complemented
59	C₂×#11483	C₂²	1	1	yes	characteristic, complemented
60	#130785	C₂²	1	8	yes	complemented
61	#130782	C₂²	1	8	yes	complemented
62	#130776	C₂²	1	8	yes	complemented
63	#130296	C₂²	1	8	yes	complemented
64	#130290	C₂²	1	8	yes	complemented
65	#130288	C₂²	1	8	yes	complemented
66	#129613	C₂²	1	8	yes	complemented
67	C₂²×#576	D₄	1	1	yes	characteristic
68	C₂²×#576	C₂³	1	1	yes	characteristic
69	C₂²×#575	D₄	1	1	yes	characteristic
70	C₂⁴×D₈	D₄	1	1	yes	characteristic
71	C₂×#3481	D₄	1	1	yes	characteristic
72	C₂×#3407	C₂³	1	1	yes	characteristic, complemented
73	#62334	D₄	1	4	yes	—
74	#62334	C₂³	1	4	yes	—
75	#62283	D₄	1	4	yes	—
76	#62283	C₂³	1	4	yes	—
77	#62269	D₄	1	4	yes	—
78	#62269	C₂³	1	4	yes	—
79	#61079	D₄	1	4	yes	—
80	#61079	C₂³	1	4	yes	—
81	#61063	D₄	1	4	yes	—
82	#61063	C₂³	1	4	yes	—
83	#61049	D₄	1	4	yes	—
84	#61049	C₂³	1	4	yes	—
85	C₂×#3263	D₄	1	1	yes	characteristic
86	C₂×#3263	D₄	1	1	yes	characteristic
87	C₂×#3263	D₄	1	1	yes	characteristic
88	C₂×#3259	D₄	1	1	yes	characteristic
89	C₂×#3256	D₄	1	1	yes	characteristic
90	C₂×#3253	D₄	1	1	yes	characteristic
91	C₂×#3204	D₄	1	1	yes	characteristic
92	C₂×#3199	D₄	1	1	yes	characteristic
93	C₂×#3197	D₄	1	1	yes	characteristic
94	C₂×#3195	D₄	1	1	yes	characteristic
95	C₂×#3192	D₄	1	1	yes	characteristic
96	C₂×#3192	D₄	1	1	yes	characteristic
97	C₂×#3155	D₄	1	1	yes	characteristic
98	C₂×#3155	D₄	1	1	yes	characteristic
99	C₂×#3150	D₄	1	1	yes	characteristic
100	C₂×#3060	D₄	1	1	yes	characteristic
101	C₂×#3060	C₂³	1	1	yes	characteristic
102	C₂×#3060	C₂³	1	1	yes	characteristic
103	C₂×#3058	C₂³	1	1	yes	characteristic
104	C₂²×#469	D₄	1	1	yes	characteristic
105	C₂×#3050	D₄	1	1	yes	characteristic
106	#60314	D₄	1	4	yes	—
107	#60314	C₂³	1	4	yes	—
108	C₂×#2980	D₄	1	1	yes	characteristic
109	C₂×#2978	D₄	1	1	yes	characteristic
110	C₂×#2977	D₄	1	1	yes	characteristic
111	C₂×#2952	D₄	1	1	yes	characteristic
112	C₂×#2948	D₄	1	1	yes	characteristic
113	C₂²×#442	D₄	1	1	yes	characteristic
114	C₂×#2932	C₂³	1	1	yes	characteristic
115	C₂×#2930	C₂³	1	1	yes	characteristic
116	C₂×#2929	C₂³	1	1	yes	characteristic
117	C₂×#2916	C₂³	1	1	yes	characteristic, complemented
118	#33659	C₂³	1	4	yes	complemented
119	#33659	C₂³	1	4	yes	complemented
120	#33657	C₂³	1	4	yes	complemented
121	#33392	C₂³	1	4	yes	complemented
122	C₂×#2115	C₂³	1	1	yes	characteristic, complemented
123	C₂×#2115	C₂³	1	1	yes	characteristic, complemented
124	C₂×#2115	C₂³	1	1	yes	characteristic, complemented
125	#27694	C₂³	1	4	yes	complemented
126	#27692	C₂³	1	4	yes	complemented
127	#27691	C₂³	1	4	yes	complemented
128	C₂×#1813	C₂³	1	1	yes	characteristic, complemented
129	C₂×#1813	C₂³	1	1	yes	characteristic, complemented
130	C₂×#1812	C₂³	1	1	yes	characteristic, complemented
131	#13079	C₂³	1	4	yes	complemented
132	#13077	C₂³	1	4	yes	complemented
133	#13076	C₂³	1	4	yes	complemented
134	#12989	C₂³	1	4	yes	complemented
135	#12988	C₂³	1	4	yes	complemented
136	#12981	C₂³	1	4	yes	complemented
137	#12810	C₂³	1	4	yes	complemented
138	#12806	C₂³	1	4	yes	complemented
139	#12805	C₂³	1	4	yes	complemented
140	#12743	C₂³	1	4	yes	complemented
141	#12743	C₂³	1	4	yes	complemented
142	#12741	C₂³	1	4	yes	complemented
143	#11872	C₂³	1	4	yes	complemented
144	#11872	C₂³	1	4	yes	complemented
145	#11872	C₂³	1	4	yes	complemented
146	#11870	C₂³	1	4	yes	complemented
147	#11868	C₂³	1	4	yes	complemented
148	#11867	C₂³	1	4	yes	complemented
149	#11486	C₂³	1	4	yes	complemented
150	#11484	C₂³	1	4	yes	complemented
151	#11483	C₂³	1	4	yes	complemented
152	C₂×#576	C₂×D₄	1	4	yes	—
153	C₂×#576	C₂×D₄	1	2	yes	—
154	C₂×#576	C₂×D₄	1	2	yes	—
155	C₂×#576	C₂×D₄	1	2	yes	—
156	C₂×#576	C₂⁴	1	2	yes	—
157	C₂×#575	C₂×D₄	1	4	yes	—
158	C₂²×#135	C₂×D₄	1	1	yes	characteristic
159	C₂²×#135	C₂×D₄	1	1	yes	characteristic
160	C₂²×#135	C₂×D₄	1	1	yes	characteristic
161	C₂²×#135	C₂×D₄	1	1	yes	characteristic
162	C₂²×#135	C₂×D₄	1	1	yes	characteristic
163	C₂³×D₈	C₂×D₄	1	1	yes	characteristic
164	C₂³×D₈	C₂×D₄	1	1	yes	characteristic
165	C₂³×D₈	C₂×D₄	1	4	yes	—
166	C₂³×D₈	C₂×D₄	1	1	yes	characteristic
167	C₂³×D₈	C₂×D₄	1	1	yes	characteristic
168	C₂²×#131	C₂×D₄	1	1	yes	characteristic
169	C₂²×#131	C₂⁴	1	1	yes	characteristic
170	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
171	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
172	#3481	SD₁₆	1	4	yes	—
173	#3481	C₂×D₄	1	4	yes	—
174	C₂×#559	SD₁₆	1	1	yes	characteristic
175	C₂×#551	SD₁₆	1	1	yes	characteristic
176	C₂×#551	SD₁₆	1	1	yes	characteristic
177	C₂×D₄²	SD₁₆	1	1	yes	characteristic
178	C₂×#532	C₂×D₄	1	1	yes	characteristic
179	C₂×#525	C₂×D₄	1	1	yes	characteristic
180	C₂×#525	C₂×D₄	1	1	yes	characteristic
181	#3407	C₂⁴	1	2	yes	complemented
182	#3263	C₂×D₄	1	4	yes	—
183	#3263	C₂×D₄	1	4	yes	—
184	#3263	C₂×D₄	1	4	yes	—
185	#3259	C₂×D₄	1	4	yes	—
186	#3256	C₂×D₄	1	4	yes	—
187	#3253	C₂×D₄	1	4	yes	—
188	#3204	C₂×D₄	1	4	yes	—
189	#3199	C₂×D₄	1	4	yes	—
190	#3197	C₂×D₄	1	4	yes	—
191	#3195	C₂×D₄	1	4	yes	—
192	#3192	C₂×D₄	1	4	yes	—
193	#3192	C₂×D₄	1	4	yes	—
194	#3155	C₂×D₄	1	4	yes	—
195	#3155	C₂×D₄	1	4	yes	—
196	#3150	C₂×D₄	1	4	yes	—
197	#3060	C₂×D₄	1	2	yes	—
198	#3060	C₂×D₄	1	2	yes	—
199	#3060	C₂×D₄	1	2	yes	—
200	#3060	C₂×D₄	1	2	yes	—
201	#3060	C₂×D₄	1	4	yes	—
202	#3060	C₂×D₄	1	2	yes	—
203	#3060	C₂×D₄	1	2	yes	—
204	#3060	C₂⁴	1	2	yes	—
205	#3060	C₂⁴	1	2	yes	—
206	#3058	C₂×D₄	1	2	yes	—
207	#3058	C₂×D₄	1	2	yes	—
208	#3058	C₂×D₄	1	2	yes	—
209	#3058	C₂⁴	1	2	yes	—
210	C₂×#470	C₂×D₄	1	1	yes	characteristic
211	C₂×#470	C₂×D₄	1	1	yes	characteristic
212	C₂×#470	C₂×D₄	1	1	yes	characteristic
213	C₂×#470	C₂×D₄	1	1	yes	characteristic
214	C₂×#469	C₂×D₄	1	1	yes	characteristic
215	C₂×#469	C₂×D₄	1	1	yes	characteristic
216	C₂×#469	C₂×D₄	1	1	yes	characteristic
217	C₂×#469	C₂×D₄	1	1	yes	characteristic
218	C₂×#469	C₂×D₄	1	1	yes	characteristic
219	C₂×#469	C₂×D₄	1	1	yes	characteristic
220	C₂×#469	C₂×D₄	1	1	yes	characteristic
221	C₂×#469	C₂×D₄	1	1	yes	characteristic
222	C₂×#469	C₂×D₄	1	4	yes	—
223	#3050	C₂×D₄	1	4	yes	—
224	#2980	C₂×D₄	1	4	yes	—
225	#2978	C₂×D₄	1	4	yes	—
226	#2977	C₂×D₄	1	4	yes	—
227	#2952	C₂×D₄	1	4	yes	—
228	#2948	C₂×D₄	1	4	yes	—
229	C₂×#442	C₂×D₄	1	4	yes	—
230	#2932	C₂×D₄	1	2	yes	—
231	#2932	C₂×D₄	1	2	yes	—
232	#2932	C₂×D₄	1	2	yes	—
233	#2932	C₂⁴	1	2	yes	—
234	#2930	C₂×D₄	1	2	yes	—
235	#2930	C₂×D₄	1	2	yes	—
236	#2930	C₂×D₄	1	2	yes	—
237	#2930	C₂⁴	1	2	yes	—
238	#2929	C₂×D₄	1	2	yes	—
239	#2929	C₂×D₄	1	2	yes	—
240	#2929	C₂×D₄	1	2	yes	—
241	#2929	C₂⁴	1	2	yes	—
242	#2916	C₂⁴	1	2	yes	complemented
243	C₂×#427	C₂×D₄	1	1	yes	characteristic
244	C₂²×#106	C₂×D₄	1	1	yes	characteristic
245	C₂²×#106	C₂×D₄	1	1	yes	characteristic
246	C₂×#424	C₂×D₄	1	1	yes	characteristic
247	C₂×#424	C₂×D₄	1	1	yes	characteristic
248	C₂×#423	C₂×D₄	1	1	yes	characteristic
249	C₂×#408	C₂×D₄	1	1	yes	characteristic
250	C₂×#408	C₂×D₄	1	1	yes	characteristic
251	C₂×#408	C₂×D₄	1	1	yes	characteristic
252	C₂×#408	C₂×D₄	1	1	yes	characteristic
253	C₂×#407	C₂×D₄	1	1	yes	characteristic
254	C₂×#407	C₂×D₄	1	1	yes	characteristic
255	C₂×#405	C₂×D₄	1	1	yes	characteristic
256	C₂×#405	C₂×D₄	1	1	yes	characteristic
257	C₂²×#97	C₂×D₄	1	1	yes	characteristic
258	#2115	C₂⁴	1	2	yes	complemented
259	#2115	C₂⁴	1	2	yes	complemented
260	#2115	C₂⁴	1	2	yes	complemented
261	#1813	C₂⁴	1	2	yes	complemented
262	#1813	C₂⁴	1	2	yes	complemented
263	#1812	C₂⁴	1	2	yes	complemented
264	C₂²×#41	#120	1	1	yes	characteristic
265	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
266	C₂⁴×C₄	#120	1	1	yes	characteristic
267	C₂⁴×C₄	#120	1	1	yes	characteristic
268	C₂×#135	#120	1	2	yes	—
269	C₂×#135	#120	1	2	yes	—
270	C₂×#135	#120	1	2	yes	—
271	C₂×#135	#120	1	2	yes	—
272	C₂×#135	#120	1	2	yes	—
273	C₂×#135	C₂²×D₄	1	2	yes	—
274	C₂×#135	C₂²×D₄	1	2	yes	—
275	C₂×#135	C₂²×D₄	1	2	yes	—
276	C₂×#135	C₂²×D₄	1	2	yes	—
277	C₂×#135	C₂²×D₄	1	2	yes	—
278	C₂²×Q₁₆	#120	1	1	yes	characteristic
279	C₂²×Q₁₆	#120	1	1	yes	characteristic
280	C₂²×Q₁₆	#120	1	1	yes	characteristic
281	C₂²×D₈	#120	1	1	yes	characteristic
282	C₂²×D₈	#120	1	1	yes	characteristic
283	C₂²×D₈	#120	1	2	yes	—
284	C₂²×D₈	#120	1	2	yes	—
285	C₂²×D₈	#120	1	1	yes	characteristic
286	C₂²×D₈	#120	1	1	yes	characteristic
287	C₂²×D₈	#120	1	1	yes	characteristic
288	C₂²×D₈	#120	1	1	yes	characteristic
289	C₂²×D₈	#120	1	1	yes	characteristic
290	C₂²×D₈	#120	1	2	yes	—
291	C₂²×D₈	#120	1	2	yes	—
292	C₂²×D₈	C₂²×D₄	1	2	yes	—
293	C₂²×D₈	C₂²×D₄	1	2	yes	—
294	C₂²×D₈	C₂²×D₄	1	2	yes	—
295	C₂²×D₈	C₂²×D₄	1	2	yes	—
296	C₂×#131	#120	1	2	yes	—
297	C₂×#131	C₂²×D₄	1	2	yes	—
298	C₂×#131	C₂²×D₄	1	1	yes	characteristic
299	C₂×#131	C₂²×D₄	1	1	yes	characteristic
300	C₂×#131	C₂²×D₄	1	1	yes	characteristic
301	C₂×#131	C₂²×D₄	1	1	yes	characteristic
302	C₂×#131	C₂²×D₄	1	1	yes	characteristic
303	C₂×#131	C₂²×D₄	1	1	yes	characteristic
304	C₂×#131	C₂²×D₄	1	1	yes	characteristic
305	C₂×#131	C₂⁵	1	1	yes	characteristic
306	C₂²×M₁₆	#120	1	1	yes	characteristic
307	C₂²×M₁₆	#120	1	1	yes	characteristic
308	C₂²×M₁₆	#120	1	1	yes	characteristic
309	C₂²×M₁₆	#120	1	2	yes	—
310	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
311	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
312	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
313	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
314	C₂³×C₈	#120	1	2	yes	—
315	C₂³×C₈	#120	1	1	yes	characteristic
316	C₂³×C₈	#120	1	1	yes	characteristic
317	C₂³×C₈	#120	1	1	yes	characteristic
318	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
319	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
320	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₈	C₂²×D₄	1	2	yes	—
322	#559	C₂×SD₁₆	1	4	yes	—
323	#551	C₂×SD₁₆	1	4	yes	—
324	#551	C₂×SD₁₆	1	4	yes	—
325	D₄²	C₂×SD₁₆	1	4	yes	—
326	#532	#120	1	2	yes	—
327	#532	C₂×SD₁₆	1	2	yes	—
328	#532	AGL(1,ℤ/8)	1	2	yes	—
329	#532	C₂²×D₄	1	2	yes	—
330	C₂×C₄⋊Q₈	AGL(1,ℤ/8)	1	1	yes	characteristic
331	C₂×#127	C₂×SD₁₆	1	1	yes	characteristic
332	C₂×#124	C₂×SD₁₆	1	1	yes	characteristic
333	C₂×#124	AGL(1,ℤ/8)	1	1	yes	characteristic
334	#525	#120	1	2	yes	—
335	#525	#120	1	2	yes	—
336	#525	C₂×SD₁₆	1	2	yes	—
337	#525	C₂×SD₁₆	1	2	yes	—
338	#525	AGL(1,ℤ/8)	1	2	yes	—
339	#525	AGL(1,ℤ/8)	1	2	yes	—
340	#525	C₂²×D₄	1	2	yes	—
341	#525	C₂²×D₄	1	2	yes	—
342	C₂×#123	C₂×SD₁₆	1	1	yes	characteristic
343	C₂×#123	C₂×SD₁₆	1	1	yes	characteristic
344	C₂×#123	AGL(1,ℤ/8)	1	1	yes	characteristic
345	C₂×#123	AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₂×#120	C₂×SD₁₆	1	1	yes	characteristic
347	C₂×#120	C₂×SD₁₆	1	1	yes	characteristic
348	C₂×#120	AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₂×#120	AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₂×#117	#120	1	1	yes	characteristic
351	C₂×#117	#120	1	1	yes	characteristic
352	C₂²×C₄²	#120	1	1	yes	characteristic
353	#470	#120	1	2	yes	—
354	#470	#120	1	2	yes	—
355	#470	#120	1	2	yes	—
356	#470	#120	1	2	yes	—
357	#470	C₂²×D₄	1	2	yes	—
358	#470	C₂²×D₄	1	2	yes	—
359	#470	C₂²×D₄	1	2	yes	—
360	#470	C₂²×D₄	1	2	yes	—
361	#469	#120	1	2	yes	—
362	#469	#120	1	2	yes	—
363	#469	#120	1	2	yes	—
364	#469	#120	1	2	yes	—
365	#469	#120	1	2	yes	—
366	#469	#120	1	2	yes	—
367	#469	#120	1	2	yes	—
368	#469	#120	1	2	yes	—
369	#469	C₂²×D₄	1	2	yes	—
370	#469	C₂²×D₄	1	2	yes	—
371	#469	C₂²×D₄	1	2	yes	—
372	#469	C₂²×D₄	1	2	yes	—
373	#469	C₂²×D₄	1	2	yes	—
374	#469	C₂²×D₄	1	2	yes	—
375	#469	C₂²×D₄	1	2	yes	—
376	#469	C₂²×D₄	1	2	yes	—
377	#427	#120	1	2	yes	—
378	#427	C₂²×D₄	1	2	yes	—
379	C₂×#106	#120	1	1	yes	characteristic
380	C₂×#106	#120	1	1	yes	characteristic
381	C₂×#106	#120	1	1	yes	characteristic
382	C₂×#106	#120	1	1	yes	characteristic
383	C₂×#106	#120	1	1	yes	characteristic
384	C₂×#106	#120	1	2	yes	—
385	C₂×#106	#120	1	2	yes	—
386	C₂×#106	#120	1	1	yes	characteristic
387	C₂×#106	C₂²×D₄	1	2	yes	—
388	C₂×#106	C₂²×D₄	1	2	yes	—
389	#424	#120	1	2	yes	—
390	#424	#120	1	2	yes	—
391	#424	C₂²×D₄	1	2	yes	—
392	#424	C₂²×D₄	1	2	yes	—
393	#423	#120	1	2	yes	—
394	#423	C₂²×D₄	1	2	yes	—
395	#408	#120	1	2	yes	—
396	#408	#120	1	2	yes	—
397	#408	#120	1	2	yes	—
398	#408	#120	1	2	yes	—
399	#408	C₂²×D₄	1	2	yes	—
400	#408	C₂²×D₄	1	2	yes	—
401	#408	C₂²×D₄	1	2	yes	—
402	#408	C₂²×D₄	1	2	yes	—
403	#407	#120	1	2	yes	—
404	#407	#120	1	2	yes	—
405	#407	C₂²×D₄	1	2	yes	—
406	#407	C₂²×D₄	1	2	yes	—
407	#405	#120	1	2	yes	—
408	#405	#120	1	2	yes	—
409	#405	C₂²×D₄	1	2	yes	—
410	#405	C₂²×D₄	1	2	yes	—
411	C₂×#97	#120	1	2	yes	—
412	C₂×#97	C₂²×D₄	1	2	yes	—
413	C₂⁵	#450	1	1	yes	characteristic
414	C₂⁵	#450	1	1	yes	characteristic
415	C₂×#41	#450	1	2	yes	—
416	C₂×#41	C₂×#120	1	2	yes	—
417	C₂×#41	C₂×#120	1	1	yes	characteristic
418	C₂×#41	C₂×#120	1	1	yes	characteristic
419	C₂×#41	C₂×#120	1	1	yes	characteristic
420	C₂×#41	C₂²×SD₁₆	1	1	yes	characteristic
421	C₂×#41	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
422	C₂×#41	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂×#41	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
424	C₂×#41	C₂³×D₄	1	1	yes	characteristic
425	C₂²×Q₈	#450	1	1	yes	characteristic
426	C₂²×Q₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
427	C₂²×D₄	#450	1	1	yes	characteristic
428	C₂²×D₄	C₂²×SD₁₆	1	1	yes	characteristic
429	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
430	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₂³×C₄	#450	1	1	yes	characteristic
432	C₂³×C₄	#450	1	2	yes	—
433	C₂³×C₄	#450	1	1	yes	characteristic
434	C₂³×C₄	#450	1	2	yes	—
435	C₂³×C₄	C₂×#120	1	1	yes	characteristic
436	C₂³×C₄	C₂×#120	1	1	yes	characteristic
437	C₂³×C₄	C₂×#120	1	1	yes	characteristic
438	C₂³×C₄	C₂×#120	1	2	yes	—
439	C₂³×C₄	C₂×#120	1	2	yes	—
440	C₂×Q₁₆	C₂×#120	1	2	yes	—
441	C₂×Q₁₆	C₂×#120	1	2	yes	—
442	C₂×Q₁₆	C₂×#120	1	2	yes	—
443	C₂×D₈	#458	1	2	yes	—
444	C₂×D₈	#458	1	2	yes	—
445	C₂×D₈	C₂×#120	1	2	yes	—
446	C₂×D₈	C₂×#120	1	2	yes	—
447	C₂×D₈	C₂×#120	1	2	yes	—
448	C₂×D₈	C₂×#120	1	2	yes	—
449	C₂×D₈	C₂×#120	1	2	yes	—
450	C₂×D₈	C₂×#120	1	2	yes	—
451	C₂×D₈	C₂×#120	1	2	yes	—
452	C₂×M₁₆	C₂×#120	1	2	yes	—
453	C₂×M₁₆	C₂×#120	1	2	yes	—
454	C₂×M₁₆	C₂×#120	1	2	yes	—
455	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
456	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
457	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
458	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
459	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
460	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
461	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
462	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
463	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
464	C₂×M₁₆	C₂³×D₄	1	1	yes	characteristic
465	C₂×M₁₆	C₂³×D₄	1	1	yes	characteristic
466	C₂×M₁₆	C₂³×D₄	1	1	yes	characteristic
467	C₂²×C₈	C₂×#120	1	1	yes	characteristic
468	C₂²×C₈	C₂×#120	1	1	yes	characteristic
469	C₂²×C₈	C₂×#120	1	1	yes	characteristic
470	C₂²×C₈	C₂×#120	1	1	yes	characteristic
471	C₂²×C₈	C₂×#120	1	1	yes	characteristic
472	C₂²×C₈	C₂×#120	1	1	yes	characteristic
473	C₂²×C₈	C₂×#120	1	1	yes	characteristic
474	C₂²×C₈	C₂×#120	1	1	yes	characteristic
475	C₂²×C₈	C₂×#120	1	1	yes	characteristic
476	C₂²×C₈	C₂×#120	1	1	yes	characteristic
477	C₂²×C₈	C₂×#120	1	1	yes	characteristic
478	C₂²×C₈	C₂×#120	1	1	yes	characteristic
479	C₂²×C₈	C₂×#120	1	2	yes	—
480	C₂²×C₈	C₂×#120	1	2	yes	—
481	C₂²×C₈	C₂×#120	1	2	yes	—
482	C₂²×C₈	C₂×#120	1	1	yes	characteristic
483	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
484	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
485	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
486	C₄⋊Q₈	#450	1	2	yes	—
487	C₄⋊Q₈	C₂×AGL(1,ℤ/8)	1	2	yes	—
488	#127	#450	1	2	yes	—
489	#127	C₂²×SD₁₆	1	2	yes	—
490	#124	#450	1	2	yes	—
491	#124	#450	1	2	yes	—
492	#124	C₂²×SD₁₆	1	2	yes	—
493	#124	C₂×AGL(1,ℤ/8)	1	2	yes	—
494	#123	#450	1	2	yes	—
495	#123	#450	1	2	yes	—
496	#123	#450	1	2	yes	—
497	#123	#450	1	2	yes	—
498	#123	C₂²×SD₁₆	1	2	yes	—
499	#123	C₂²×SD₁₆	1	2	yes	—
500	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
501	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
502	#120	#450	1	2	yes	—
503	#120	#450	1	2	yes	—
504	#120	#450	1	2	yes	—
505	#120	#450	1	2	yes	—
506	#120	C₂²×SD₁₆	1	2	yes	—
507	#120	C₂²×SD₁₆	1	2	yes	—
508	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
509	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
510	#117	#450	1	2	yes	—
511	#117	#450	1	2	yes	—
512	#117	C₂×#120	1	2	yes	—
513	#117	C₂×#120	1	2	yes	—
514	C₂×C₂²⋊C₄	#450	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	#450	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	#450	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	#450	1	1	yes	characteristic
518	C₂×C₄²	#450	1	1	yes	characteristic
519	C₂×C₄²	#450	1	1	yes	characteristic
520	C₂×C₄²	#450	1	2	yes	—
521	C₂×C₄²	C₂×#120	1	2	yes	—
522	#106	C₂×#120	1	2	yes	—
523	#106	C₂×#120	1	2	yes	—
524	#106	C₂×#120	1	2	yes	—
525	#106	C₂×#120	1	2	yes	—
526	#106	C₂×#120	1	2	yes	—
527	#106	C₂×#120	1	2	yes	—
528	C₂⁴	C₂×#450	1	1	yes	characteristic
529	C₂⁴	C₂×#450	1	1	yes	characteristic
530	C₂⁴	C₂×#450	1	2	yes	—
531	C₂⁴	C₂×#450	1	2	yes	—
532	C₂⁴	#3003	1	1	yes	characteristic
533	C₂×Q₈	C₂×#450	1	2	yes	—
534	C₂×Q₈	C₂×#450	1	1	yes	characteristic
535	C₂×Q₈	#3003	1	1	yes	characteristic
536	C₂×Q₈	#3003	1	1	yes	characteristic
537	C₂×Q₈	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂×D₄	C₂×#450	1	1	yes	characteristic
539	C₂×D₄	C₂×#450	1	1	yes	characteristic
540	C₂×D₄	C₂×#450	1	1	yes	characteristic
541	C₂×D₄	C₂×#450	1	1	yes	characteristic
542	C₂×D₄	C₂×#450	1	2	yes	—
543	C₂×D₄	C₂×#450	1	1	yes	characteristic
544	C₂×D₄	#3003	1	1	yes	characteristic
545	C₂×D₄	#3003	1	1	yes	characteristic
546	C₂×D₄	#3003	1	1	yes	characteristic
547	C₂×D₄	#3003	1	1	yes	characteristic
548	C₂×D₄	C₂³×SD₁₆	1	1	yes	characteristic
549	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
550	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
551	C₂²×C₄	#2846	1	1	yes	characteristic
552	C₂²×C₄	#2846	1	1	yes	characteristic
553	C₂²×C₄	#2846	1	1	yes	characteristic
554	C₂²×C₄	#2846	1	1	yes	characteristic
555	C₂²×C₄	C₂×#450	1	1	yes	characteristic
556	C₂²×C₄	C₂×#450	1	1	yes	characteristic
557	C₂²×C₄	C₂×#450	1	1	yes	characteristic
558	C₂²×C₄	C₂×#450	1	1	yes	characteristic
559	C₂²×C₄	C₂×#450	1	2	yes	—
560	C₂²×C₄	C₂×#450	1	2	yes	—
561	C₂²×C₄	#3003	1	1	yes	characteristic
562	C₂²×C₄	#3003	1	1	yes	characteristic
563	C₂²×C₄	#3003	1	1	yes	characteristic
564	C₂²×C₄	#3003	1	1	yes	characteristic
565	C₂²×C₄	#3003	1	1	yes	characteristic
566	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
567	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
568	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
569	D₈	C₂×#458	1	4	yes	—
570	C₂×C₈	#2846	1	1	yes	characteristic
571	C₂×C₈	#2846	1	1	yes	characteristic
572	C₂×C₈	#2846	1	1	yes	characteristic
573	C₂×C₈	#2846	1	1	yes	characteristic
574	C₂×C₈	C₂×#458	1	1	yes	characteristic
575	C₂×C₈	C₂×#458	1	1	yes	characteristic
576	C₂×C₈	#3026	1	1	yes	characteristic
577	C₂×C₈	#3026	1	1	yes	characteristic
578	C₂×C₈	C₂²×#120	1	1	yes	characteristic
579	C₂×C₈	C₂²×#120	1	1	yes	characteristic
580	C₂×C₈	C₂²×#120	1	1	yes	characteristic
581	C₂×C₈	C₂²×#120	1	1	yes	characteristic
582	C₂²⋊C₄	C₂×#450	1	2	yes	—
583	C₂²⋊C₄	C₂×#450	1	2	yes	—
584	C₂²⋊C₄	C₂×#450	1	2	yes	—
585	C₂²⋊C₄	C₂×#450	1	2	yes	—
586	C₄²	C₂×#450	1	2	yes	—
587	C₄²	C₂×#450	1	2	yes	—
588	C₂³	#32881	1	1	yes	characteristic
589	C₂³	#32881	1	1	yes	characteristic
590	C₂³	#32881	1	1	yes	characteristic
591	C₂³	#32881	1	1	yes	characteristic
592	C₂³	C₂²×#450	1	1	yes	characteristic
593	C₂³	C₂²×#450	1	1	yes	characteristic
594	C₂³	C₂×#3003	1	1	yes	characteristic
595	C₂×C₄	#32881	1	1	yes	characteristic
596	C₂×C₄	#32881	1	1	yes	characteristic
597	C₂×C₄	#32881	1	1	yes	characteristic
598	C₂×C₄	#32881	1	1	yes	characteristic
599	C₂×C₄	#32894	1	1	yes	characteristic
600	C₂×C₄	#32894	1	1	yes	characteristic
601	C₂×C₄	#32900	1	1	yes	characteristic
602	C₂×C₄	#32900	1	1	yes	characteristic
603	C₂×C₄	C₂×#2846	1	1	yes	characteristic
604	C₂×C₄	C₂²×#450	1	1	yes	characteristic
605	C₂×C₄	C₂×#3003	1	1	yes	characteristic
606	C₂×C₄	C₂×#3003	1	1	yes	characteristic
607	C₈	#32900	1	1	yes	characteristic
608	C₈	#32900	1	1	yes	characteristic
609	C₈	C₂²×#458	1	1	yes	characteristic
610	C₈	C₂×#3026	1	1	yes	characteristic
611	C₂²	#346542	1	1	yes	characteristic
612	C₂²	#346542	1	1	yes	characteristic
613	C₂²	C₂×#32881	1	1	yes	characteristic
614	C₄	#346542	1	1	yes	characteristic
615	C₄	#346542	1	1	yes	characteristic
616	C₄	C₂×#32894	1	1	yes	characteristic
617	C₄	C₂×#32900	1	1	yes	characteristic
618	C₂	#72231700	1	2	yes	direct product factor
619	C₂	C₂×#346542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#346542
commutator, Frattini, cosocle	C₂×#131	C₂⁵
prime radical	C₂×#10583240	C₂
LCS	G ▷ C₂×#131 ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#131 ◁ G
LECS	G ▷ C₂×#131 ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#500158	C₂	semidirect
2. C₂×#512046	C₂	semidirect
3. C₂×#130785	C₂	semidirect
4. C₂×#129613	C₂	semidirect
6. C₂×#130290	C₂	semidirect
7. C₂×#486694	C₂	semidirect
8. C₂×#486689	C₂	semidirect
9. C₂×#130288	C₂	semidirect
10. C₂×#130296	C₂	semidirect
11. C₂×#486701	C₂	semidirect
12. C₂×#130782	C₂	semidirect
13. C₂×#130776	C₂	semidirect
14. C₂×#500168	C₂	semidirect
15. C₂×#500164	C₂	semidirect
16. #72231700	C₂	direct (N × H)
25. C₂×#33659	C₂²	semidirect
26. C₂×#33659	C₂²	semidirect
27. C₂×#33657	C₂²	semidirect
28. C₂×#33392	C₂²	semidirect
29. C₂×#27694	C₂²	semidirect
30. C₂×#27692	C₂²	semidirect
31. C₂×#27691	C₂²	semidirect
32. #512046	C₂²	semidirect
33. #500168	C₂²	semidirect
34. #500164	C₂²	semidirect
35. #500158	C₂²	semidirect
36. C₂×#13079	C₂²	semidirect
37. C₂×#13077	C₂²	semidirect
38. C₂×#13076	C₂²	semidirect
39. C₂×#12989	C₂²	semidirect
40. C₂×#12988	C₂²	semidirect
41. C₂×#12981	C₂²	semidirect
42. C₂×#12810	C₂²	semidirect
43. C₂×#12806	C₂²	semidirect
44. C₂×#12805	C₂²	semidirect
45. C₂×#12743	C₂²	semidirect
46. C₂×#12743	C₂²	semidirect
47. C₂×#12741	C₂²	semidirect
48. #486701	C₂²	semidirect
49. #486694	C₂²	semidirect
50. #486689	C₂²	semidirect
51. C₂×#11872	C₂²	semidirect
52. C₂×#11872	C₂²	semidirect
53. C₂×#11872	C₂²	semidirect
54. C₂×#11870	C₂²	semidirect
55. C₂×#11867	C₂²	semidirect
56. C₂×#11868	C₂²	semidirect
57. C₂×#11486	C₂²	semidirect
58. C₂×#11484	C₂²	semidirect
59. C₂×#11483	C₂²	semidirect
60. #130785	C₂²	semidirect
61. #130782	C₂²	semidirect
62. #130776	C₂²	semidirect
63. #130296	C₂²	semidirect
64. #130290	C₂²	semidirect
65. #130288	C₂²	semidirect
66. #129613	C₂²	semidirect
72. C₂×#3407	C₂³	semidirect
117. C₂×#2916	C₂³	semidirect
118. #33659	C₂³	semidirect
119. #33659	C₂³	semidirect
120. #33657	C₂³	semidirect
121. #33392	C₂³	semidirect
122. C₂×#2115	C₂³	semidirect
123. C₂×#2115	C₂³	semidirect
124. C₂×#2115	C₂³	semidirect
125. #27694	C₂³	semidirect
126. #27692	C₂³	semidirect
127. #27691	C₂³	semidirect
128. C₂×#1813	C₂³	semidirect
129. C₂×#1813	C₂³	semidirect
130. C₂×#1812	C₂³	semidirect
131. #13079	C₂³	semidirect
132. #13077	C₂³	semidirect
133. #13076	C₂³	semidirect
134. #12989	C₂³	semidirect
135. #12988	C₂³	semidirect
136. #12981	C₂³	semidirect
137. #12810	C₂³	semidirect
138. #12806	C₂³	semidirect
139. #12805	C₂³	semidirect
140. #12743	C₂³	semidirect
141. #12743	C₂³	semidirect
142. #12741	C₂³	semidirect
143. #11872	C₂³	semidirect
144. #11872	C₂³	semidirect
145. #11872	C₂³	semidirect
146. #11870	C₂³	semidirect
147. #11868	C₂³	semidirect
148. #11867	C₂³	semidirect
149. #11486	C₂³	semidirect
150. #11484	C₂³	semidirect
151. #11483	C₂³	semidirect
181. #3407	C₂⁴	semidirect
242. #2916	C₂⁴	semidirect
258. #2115	C₂⁴	semidirect
259. #2115	C₂⁴	semidirect
260. #2115	C₂⁴	semidirect
261. #1813	C₂⁴	semidirect
262. #1813	C₂⁴	semidirect
263. #1812	C₂⁴	semidirect
618. C₂	#72231700	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#500158	2
C₂×#512046	2
C₂×#130785	2
C₂×#129613	2
C₂×#10583240	2
C₂×#130290	2
C₂×#486694	2
C₂×#486689	2
C₂×#130288	2
C₂×#130296	2
C₂×#486701	2
C₂×#130782	2
C₂×#130776	2
C₂×#500168	2
C₂×#500164	2
#72231700	2

Subgroups — C2×#72231700 #72310632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72231700 #72310632